Is there a link between non-locality and non-linearity?

  • Context: Graduate 
  • Thread starter Thread starter cryptist
  • Start date Start date
  • Tags Tags
    Non-linear
Click For Summary

Discussion Overview

The discussion explores the potential connections between non-locality and non-linearity in physical systems. Participants examine whether non-local systems must involve non-linear equations and if non-linear equations arise as a consequence of non-locality. The conversation touches on theoretical implications, examples from quantum mechanics, and the nature of physical laws.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants question whether non-local systems necessarily require non-linear equations, suggesting that the relationship is not straightforward.
  • One participant notes that the response of a material can be non-linear depending on external fields, while non-locality may not depend on these fields.
  • Another participant proposes that if a particle is subjected to an instantaneous effect that changes its position superluminally, this non-local system might imply non-linear equations.
  • Some participants highlight that quantum mechanics is linear and non-local, raising questions about the implications of this for the relationship between non-linearity and non-locality.
  • It is suggested that there is no direct relation between non-linearity and non-locality, although a hypothetical non-linear quantum mechanics could be more non-local than its linear counterpart.
  • Participants discuss the conditions under which non-linear equations might arise, including the dependence of a particle's position on its derivatives.
  • One participant expresses uncertainty about the implications of non-locality increasing from linear to non-linear systems.
  • There is a suggestion that the relationship between non-locality and non-linearity is more complex than initially thought, with no substantial connection established.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the relationship between non-locality and non-linearity. Multiple competing views are presented, with some arguing for a connection and others asserting a lack of direct relation.

Contextual Notes

Participants express uncertainty regarding the definitions and implications of non-locality and non-linearity, particularly in the context of quantum mechanics. The discussion includes unresolved questions about the nature of these concepts and their interrelations.

cryptist
Messages
121
Reaction score
1
Is there a strict connection between non-locality and non-linearity? Is it true that non-local systems must have non-linear equations? Are non-linear equations the consequence of non-locality?
 
Physics news on Phys.org
Really? Isn't anyone can answer this?
 
Your question is very general.
The response of a material can be non-linear -this depends on the (external) field- while non-locality does not necessarily depend on the field. I don't know if this applies to all cases, this is simply my understanding.

cryptist said:
Is it true that non-local systems must have non-linear equations?

You need to elaborate a bit here. What kind of "non-linear equations" do you have in mind ?

cryptist said:
Are non-linear equations the consequence of non-locality?

The constitutive relations of a chiral medium can be linear and non-local.
 
Yes, and I expect a general answer. There might be some exceptional systems as you mentioned. But, can we say that in general?

Nevertheless, let's think the motion of a particle as an example. Let's assume we exposed particle to an instantaneous effect (for example that effect can change his position superluminally). Then this system is non-local, and it must have non-linear equations, right?
 
Isn't quantum mechanics linear and non-local?
 
Yes, quantum mechanics is linear, and I think that's why it cannot explain some phenomena like wave function collapse.
 
cryptist said:
Nevertheless, let's think the motion of a particle as an example. Let's assume we exposed particle to an instantaneous effect (for example that effect can change his position superluminally). Then this system is non-local, and it must have non-linear equations, right?

A non-local eqn will pop out if the particle's position does not depend only on the applied field, say F, but also on its derivatives, its curl for example. This does not necessarily* introduce nonlinearities in the eqns of motion.

* meaning that you don't always get quadratic or higher order terms of F
 
cryptist said:
Yes, quantum mechanics is linear, and I think that's why it cannot explain some phenomena like wave function collapse.

You are asking about a strict connection between non-linear and non-local. If quantum mechanics is linear and non-local, then your question has a negative answer, no?
 
There is no direct relation between nonlinearity and nonlocality.

Yet, if QM were nonlinear (not merely by a collapse postulate, but at a more physical level), then, depending on the interpretation, it could be even more nonlocal than it is in the standard linear form.
See e.g.
http://xxx.lanl.gov/abs/0707.2319
and Refs. [1,2,3] therein.
 
  • #10
|squeezed> said:
A non-local eqn will pop out if the particle's position does not depend only on the applied field, say F, but also on its derivatives, its curl for example. This does not necessarily* introduce nonlinearities in the eqns of motion.

* meaning that you don't always get quadratic or higher order terms of F

So such field should affect particle's acceleration also, to have non-linear equations?

martinbn said:
You are asking about a strict connection between non-linear and non-local. If quantum mechanics is linear and non-local, then your question has a negative answer, no?

Or quantum mechanics is wrong. Oops, I have to run :))

Demystifier said:
There is no direct relation between nonlinearity and nonlocality.

Yet, if QM were nonlinear (not merely by a collapse postulate, but at a more physical level), then, depending on the interpretation, it could be even more nonlocal than it is in the standard linear form.
See e.g.
http://xxx.lanl.gov/abs/0707.2319
and Refs. [1,2,3] therein.

So as far as I understand, although no strict connection between both, nonlocality increases from linear to nonlinear.
 
  • #11
cryptist said:
So such field should affect particle's acceleration also, to have non-linear equations?

No. Why do you say this ?


cryptist said:
So as far as I understand, although no strict connection between both, nonlocality increases from linear to nonlinear.

What do you mean by "nonlocality increases from linear to nonlinear" ?
 
  • #12
martinbn said:
Isn't quantum mechanics linear ?

not settled yet.
 
  • #13
Ok, I guess the relationship between these two is far more than I thought. So there is no substantial connection.
 

Similar threads

High School What is a non-local Hamiltonian?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad New Nobel Aspect contradicts himself on action at a distance bel
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Objective Wave Function and Non-locality
  • · Replies 33 ·
2
Replies
33
Views
3K
Undergrad Can the Lieb-Robinson Bound be Intuited from the Taylor Series of an Operator?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Qubit Energy Level Required to be Unevenly Separated
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Unruh, Haag et al.: No Room for Particles in Quantum Field Theory?
  • · Replies 12 ·
Replies
12
Views
3K
Graduate Collapse in QM: in conflict with SR?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Regarding Relativity of Simultaneity, is non-local "now" impossible?
  • · Replies 2 ·
Replies
2
Views
584
High School Bell Non Locality, Quantum Non Locality, Weak Locality, CDP
  • · Replies 80 ·
3
Replies
80
Views
9K
Graduate Quantum properties and Van Hove singularty
  • · Replies 5 ·
Replies
5
Views
544